Cycles

Cycles[{cyc1,cyc2,}]

represents a permutation with disjoint cycles cyci.

Details

  • The cycles cyci of a permutation are given as lists of positive integers, representing the points of the domain in which the permutation acts.
  • A cycle {p1,p2,,pn} represents the mapping of the pi to pi+1. The last point pn is mapped to p1.
  • Points not included in any cycle are assumed to be mapped onto themselves.
  • Cycles must be disjoint, that is, they must have no common points.
  • Cycles objects are automatically canonicalized by dropping empty and singleton cycles, rotating each cycle so that the smallest point appears first, and ordering cycles by the first point.
  • Cycles[{}] represents the identity permutation.

Examples

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Basic Examples  (2)

A permutation with two cycles:

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Automatic evaluation to a canonical form:

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Scope  (2)

Properties & Relations  (9)

Possible Issues  (3)

Neat Examples  (1)

See Also

PermutationCyclesQ  PermutationCycles  PermutationList  PermutationGroup  PermutationProduct  Permutations  FindPermutation  Permute  PermutationReplace

Tutorials

Related Demonstrations

Introduced in 2010
(8.0)